AdS_5 Solutions of Type IIB Supergravity and Generalized Complex Geometry

Abstract

We use the formalism of generalized geometry to study the generic supersymmetric AdS_5 solutions of type IIB supergravity that are dual to N=1 superconformal field theories (SCFTs) in d=4. Such solutions have an associated six-dimensional generalized complex cone geometry that is an extension of Calabi-Yau cone geometry. We identify generalized vector fields dual to the dilatation and R-symmetry of the dual SCFT and show that they are generalized holomorphic on the cone. We carry out a generalized reduction of the cone to a transverse four-dimensional space and show that this is also a generalized complex geometry, which is an extension of Kahler-Einstein geometry. Remarkably, provided the five-form flux is non-vanishing, the cone is symplectic. The symplectic structure can be used to obtain Duistermaat-Heckman type integrals for the central charge of the dual SCFT and the conformal dimensions of operators dual to BPS wrapped D3-branes. We illustrate these results using the Pilch-Warner solution.

56 pages; v2: minor changes, version to be published in Commun. Math. Phys

References in corpus (12)

• Sasaki-Einstein Manifolds and Volume Minimisation
• Dimer models and toric diagrams
• A scan for new N=1 vacua on twisted tori
• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• D-branes on general N=1 backgrounds: superpotentials and D-terms
• Gauge/Gravity Duality and Warped Resolved Conifold
• Reformulating Supersymmetry with a Generalized Dolbeault Operator
• New aspects of the ddc-lemma
• Gravity duals to deformed SYM theories and Generalized Complex Geometry
• On the geometry and the moduli space of beta-deformed quiver gauge theories
• Baryonic branches and resolutions of Ricci-flat Kahler cones
• The central charge of supersymmetric AdS_5 solutions of type IIB supergravity

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• Supersymmetric Backgrounds, the Killing Superalgebra, and Generalised Special Holonomy
• The free energy of N=2 supersymmetric AdS_4 solutions of M-theory
• Generalised Structures for $\mathcal{N}=1$ AdS Backgrounds
• Generalized Geometry in AdS/CFT and Volume Minimization
• Wilson loops and the geometry of matrix models in AdS_4/CFT_3
• Generalized geometry of two-dimensional vacua
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• Generalising G${}_{\text{2}}$ geometry: involutivity, moment maps and moduli
• Supersymmetric AdS${}_5$ solutions of type IIB supergravity without D3 branes
• A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
• AdS${}_5$ vacua from type IIB supergravity on $T^{1,1}$
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• Generalised Calibrations in AdS backgrounds from Exceptional Sasaki-Einstein Structures
• Equivalence of A-Maximization and Volume Minimization
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• Flux Backgrounds and Exceptional Generalised Geometry
• Exactly Marginal Deformations and their Supergravity Duals